OG Xbox is the first console of the modern paradigm. Its key games - Halo, Splinter Cell, Elder Scrolls etc - these are what are the main game types today.
GC and PS2 are also similar, but I think have lots of the quirky Japanese vibe from earlier Japanese consoles left, at least in a higher percentage of top games. DC to an even greater extent. And those are the types of games that appeal to retro-fans. I remember Katamari and Viewtiful Joe, not Need for Speed Underground (despite the latter being the higher seller). Xbox has some of these quirky too, but not as many (and of course the GCN has Nintendo who even today make more 'retro' games then almost everyone except indies). But GC and PS2 don't feel too retro to me either for a similar reason.
Microsoft didn't make any money, but with their spending they did manage to push change of what a console is - a western-focused PC in a box type thing. The PS4 is more a 'latest' Xbox style console than a new PS1 IMO.
Maybe I'm just a Japanese fetishist though.
Xbox had its share of fun Japanese games too:
JSRF, Panzer Dragoon Orta, Phantom Dust, Shenmue II, Otogi 1 and 2, Ninja Gaiden and NGBlack, DOA 3 Ultimate and Xtrreme, Gunvalkyrie, Metal Slug 3-5, SVC Chaos: SNK vs. Capcom, Capcom vs. SNK 2, Silent Scope Complete, Crazy Taxi 3, Sega Soccer Slam, Dynasty Warriors 3-5, Fatal Frame 1 and 2, Marvel vs. Capcom 2, Mega Man Anniversary Collection, Metal Gear Solid 2: Substance, Phantasy Star Online 1 & 2, Phantom Crash, Samurai Showdown V, Sega GT 2002, Sega GT Online, Soul Calibur II, Sonic Heroes, Sonic Mega Collection Plus, Sonic Riders, Steel Battalion, Steel Battalion: Line of Contact, Street Fighter Anniversary Collection, Super Monkey Ball Deluxe... etc.
That's a pretty worthy library of Japanese games. Forget the fact that you could also play Halo, Morrowind, Kotor, Jade Empire, PGR and other fantastic western console exclusives on it.
I'd venture to say that it has a library that is equal in quality to GCN, DC, and in many ways, even the mighty PS2.